Pope Francis perked up ears again Wednesday when he advised church leadership to do more to “take care” of and have “open doors” for Catholics whose marriages have failed, prompting the latest round of speculation — both hopeful and worrying — that he may loosen the church’s ancient rules on divorce and remarriage.

Although the pope acknowledged in his Vatican City remarks that “a new union” after divorce “contradicts the Christian sacrament,” the call to rein in judgment of divorced Catholics the latest example of his “pastoral” approach to the church’s teachings on sex, which, along with his environmentalism and vigorous critiques of capitalism, have made him relatively popular among Western progressives.

The church, Francis said, should always draw “from her heart of mother,” which, animated by the Holy Spirit, always seeks “the good and the salvation of the person.”

“People who started a new union after the defeat of their sacramental marriage are not at all excommunicated, and they absolutely must not be treated that way,” the pontiff told pilgrims and tourists at his first general audience after a summer break. “They always belong to the church,” he said.

The Catholic Church teaches that a valid marriage is permanent until death and that subsequent marriages, even if there is a secular divorce, are impossible and put both parties in a state of mortal sin as adulterers. At one time, church practice went so far as refusing to ordain men who were born outside a legitimate marriage.

Bill Donohue, president of the Catholic League for Religious and Civil Rights, said Francis is ensuring that divorced and remarried Catholics “know that they have not been excommunicated and are indeed welcomed in the Church.”

“That they cannot take Holy Communion (unless they receive an annulment from their first marriage) remains unchanged,” Mr. Donohue, a sociologist and conservative civil activist, said Wednesday.

Thus, even though the pope continues his outreach to disaffected Catholics, his position “changes nothing doctrinally; it is purely of pastoral significance. Which means there is no reason for the secular media to hyperventilate,” Mr. Donohue said.

Anthony Padovano, a Catholic scholar and board member of Catholics for Choice, said Francis is choosing not to act unilaterally to change church doctrine on divorce and remarriage. He actually wants the bishops to “stand up and ask” for divorce reforms.

But the pope instead is giving local clergy “incredible latitude” to welcome Catholics, he said.

Some priests already quietly permit some remarried Catholics to receive Communion, and now Francis’ words will make it “very difficult” for bishops or others to say that is always wrong, said Mr. Padovano, who holds doctorates and professorships in theology and literature.

Conservative or liberal?

American Catholics and others will be listening closely in September when Francis visits the U.S. and speaks at the White House, in Congress, in New York and, most directly relevant to this topic, at the World Meeting of Families in Philadelphia.

He has voiced views that have prompted head-scratching — leaning conservative in some cases and liberal in others.

“Pope Francis is affectionately known as our ‘holy conundrum,’” said Linda Pinto, co-editor of a report for the Catholic reform group Corpus, according to Catholics for Choice.

Ms. Pinto and other reformers met at a July conference in Chicago to talk about how to influence the Catholic Church in its views and policies on women. But the progressive side of Francis has many dimensions.

For instance, Francis has, by name, denounced “trickle-down economics” and income inequality, and he issued an encyclical this year endorsing global warming theories. In one passage, he said people overuse air conditioning.

On matters relating to homosexuality, he famously said in 2013, “if they accept the Lord and have good will, who am I to judge?” when asked about gays who “search for the Lord.” He suggested — both as pontiff and as Archbishop Jorge Bergoglio of Buenos Aires — that the church could accept civil unions.

On contraception, he called 1967’s Humanae Vitae encyclical against it “prophetic” but said the church needs to be “making sure that pastoral action takes into account that which is possible for people to do.”

In one of his most famous quips, he derided the idea that “in order to be good Catholics, we have to be like rabbits.”

Francis also has made personal action in using the sacraments of the church to demonstrate what he calls a “pastoral” approach on human sexuality. Shortly after becoming pope in 2013, he told an unwed pregnant woman that he would baptize her baby, and used the Sistine Chapel to baptize the baby of a couple who were married civilly but not in the church.

These comments have animated countless discussions and internal debates among clergy — and the faithful.

A Gallup Poll in July of more than 1,000 adults found that Catholic support for Francis had fallen from 89 percent in 2014 to 71 percent in 2015.

The erosion was even steeper among Americans who are politically conservative. Their favorable views dropped from 72 percent to 45 percent in that time frame.

Catholic author James Hitchcock, who opposes changing church practices on this matter, told The Associated Press that Francis “leans in the direction of ‘Let’s loosen our discipline on this’” but doesn’t seem to think things through.

“He is not a systematic thinker. I don’t think he sits down and works this all out. I think he follows his heart. I think he says things in a way he thinks will be inspirational or helpful and then we can work that all out later,” he said.

Divorce reforms discussion

Divorce reform will be a topic at two upcoming conferences for Catholic leaders — the Philadelphia meeting in September and the Synod of Bishops on the Family in Vatican City in October.

Discussions will revolve around the sacredness and indissolubility of marriage and the reality of millions of divorced and remarried Catholics who are distressed by their exclusion from Communion or church leadership.

Estranged Catholic couples may seek annulments, or declarations by the church that the marriages were never valid. One may be granted based on such acts as deliberate deceit, “psychic incapacity” and grave violations of fidelity in the marriage or childbearing. The process can be lengthy, often involves a large fee, and is viewed as too intrusive by some people.

Secular divorce is allowed — the church has no say in state marriage, and the Catechism even acknowledges that it can be the least-bad alternative — but remarriage is not.

Catholics who remarry without the church annulling previous unions are deemed to be publicly living in sin and engaged in scandal, and thus not permitted to take Holy Communion. However, their children may do so, as well as be baptized, be confirmed and be ordained.

In his earlier comments on divorce, Francis said the annulment fees should be eliminated and that the annulment process be handled more efficiently. He also said in 2013, while flying back to Rome from a trip to South America, that the divorce issue “is complicated.”

“I believe this is a time of mercy, a change of epoch,” Francis said. “In terms of Communion for those who have divorced and remarried, it has to be seen within the largest pastoral context of marriage.”

Words like these have sparked hopes that the rules on Communion will be changed for remarried Catholics. However, in his Aug. 5 remarks at St. Peter’s Square, Francis didn’t go that far — although he again called for an attitude change in the church.

Priests are advised to use “discernment” in couples’ situations, and appreciate the differences between partners who “provoked” the breakup and partners who “suffered,” Francis said.

Moreover, he pointed out, how can parents educate their children in Christian life “if we keep them at a distance as if they were excommunicated?”

The divorced and remarried “can live and develop ever more” their relationships with Christ and the church through prayer, listening to the Word of God, attendance at the liturgy, the Christian education of their children, performing charity and service to the poor and calling for justice and peace, Francis said Wednesday.

Pastors also can help children by not adding “weight beyond what the children in this situation have to bear,” he said.

• Victor Morton contributed to this article, which is based in part on wire service reports.